Rate of convergence for the Smoluchowski–Kramers approximation for distribution-dependent SDEs driven by fractional Brownian motions

2024/02/01 by Wei Liu, Bin Pei, Qian Yu
Economics, Econometrics and Finance · Mathematics · #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #Financial Risk and Volatility Modeling

paper · doi:10.1142/s0219493724500023

Abstract

In this paper, we study the rate in the Smoluchowski–Kramers approximation for the solution of the following distribution-dependent SDE driven by fractional Brownian motion [Formula: see text] where [Formula: see text] denotes the law of [Formula: see text], [Formula: see text] is a [Formula: see text]-dimensional fractional Brownian motion with Hurst parameter [Formula: see text]. Based on the techniques of multiple integrals and Malliavin calculus, we provide an explicit bound on total variation distance for the rate of convergence.

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